Group #19136629 — subgroups

Subgroups — #19136629

Order 5504.

186 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 49 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×D₆₈₈	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#13063266	C₂	1	1	yes	maximal, characteristic, complemented
3	#14583274	C₂	1	1	yes	maximal, characteristic, complemented
4	#14582981	C₂	1	1	yes	maximal, characteristic, complemented
5	Dic₄₃⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
6	#14582699	C₂	1	1	yes	maximal, characteristic, complemented
7	C₄₃×#357	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
9	C₂×D₃₄₄	C₂²	1	1	yes	characteristic
10	C₂×#10621882	—	2	1	no	—
11	#13063321	—	2	1	no	—
12	#13063287	—	2	1	no	—
13	D₆₈₈	—	2	2	no	—
14	#13063266	—	2	2	no	—
15	C₂×C₄₃⋊C₁₆	C₂²	1	1	yes	characteristic
16	#13063245	—	2	1	no	—
17	C₈×Dic₄₃	C₂²	1	1	yes	characteristic
18	C₂×D₈×C₄₃	C₂²	1	1	yes	characteristic
19	C₂×C₁₆×C₄₃	C₂²	1	1	yes	characteristic
20	#107×C₄₃	C₂²	1	1	yes	characteristic
21	C₂×D₄×C₄₃	—	2	1	no	—
22	C₂×C₂²⋊D₄₃	—	4	1	no	—
23	C₂×C₂²⋊D₄₃	—	4	1	no	—
24	C₂×D₁₇₂	—	2	1	no	—
25	C₂×D₁₇₂	—	2	1	no	—
26	C₂×C₄×D₄₃	—	4	1	no	—
27	D₈×C₄₃	—	2	1	no	—
28	D₈×C₄₃	—	2	1	no	—
29	C₂×C₈×C₄₃	C₂³	1	1	yes	characteristic
30	C₄⋊C₄×C₄₃	—	2	1	no	—
31	#10621882	—	4	2	no	—
32	(C₂×D₄₃)⋊C₄	—	4	1	no	—
33	C₄×Dic₄₃	D₄	1	1	yes	characteristic
34	C₂×C₄₃⋊C₈	D₄	1	1	yes	characteristic
35	D₃₄₄	—	2	1	no	—
36	D₃₄₄	—	2	1	no	—
37	D₃₄₄	—	2	1	no	—
38	D₃₄₄	D₄	1	2	yes	complemented
39	C₁₆×C₄₃	—	2	1	no	—
40	C₄₃⋊C₁₆	—	2	1	no	—
41	C₂³×C₄₃	—	4	1	no	—
42	C₂²×D₄₃	—	4	1	no	—
43	C₂²×D₄₃	—	4	1	no	—
44	D₄×C₄₃	—	4	1	no	—
45	D₄×C₄₃	—	4	1	no	—
46	C₂×C₄×C₄₃	—	4	1	no	—
47	C₂×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
48	C₂²⋊D₄₃	—	8	2	no	—
49	C₂²⋊D₄₃	—	8	2	no	—
50	C₂×Dic₄₃	D₈	1	1	yes	characteristic
51	C₂×Dic₄₃	D₈	1	1	yes	characteristic
52	D₁₇₂	—	2	2	no	—
53	D₁₇₂	—	4	1	no	—
54	D₁₇₂	—	4	1	no	—
55	D₁₇₂	—	4	1	no	—
56	C₄×D₄₃	—	8	2	no	—
57	C₈×C₄₃	C₂×D₄	1	1	yes	characteristic
58	C₈×C₄₃	#41	1	1	yes	characteristic
59	C₄₃⋊C₈	—	2	1	no	—
60	C₂²×C₄₃	—	8	1	no	—
61	C₂²×C₄₃	—	8	1	no	—
62	C₂²×C₄₃	—	8	1	no	—
63	C₂²×C₄₃	C₂×D₈	1	1	yes	characteristic
64	C₂×D₄₃	—	4	2	no	—
65	C₂×D₄₃	—	8	1	no	—
66	C₂×D₄₃	—	8	1	no	—
67	C₂×D₄₃	—	8	1	no	—
68	C₂×D₄₃	—	8	1	no	—
69	C₂×D₄₃	—	8	1	no	—
70	C₄×C₄₃	—	8	1	no	—
71	C₄×C₄₃	#121	1	1	yes	characteristic
72	C₄×C₄₃	AGL(1,ℤ/8)	1	1	yes	characteristic
73	Dic₄₃	—	2	1	no	—
74	Dic₄₃	D₁₆	1	2	yes	complemented
75	#2206	—	43	1	no	maximal, Sylow
76	C₂×C₄₃	—	16	1	no	—
77	C₂×C₄₃	#459	1	1	yes	characteristic
78	C₂×C₄₃	C₂×D₁₆	1	1	yes	characteristic
79	C₂×C₄₃	#509	1	1	yes	characteristic
80	D₄₃	—	8	2	no	—
81	D₄₃	—	16	1	no	—
82	C₂×D₁₆	—	43	1	no	—
83	C₂×D₁₆	—	43	1	no	—
84	#493	—	43	1	no	—
85	C₄×D₈	—	43	1	no	—
86	C₄⋊C₁₆	—	43	1	no	—
87	#357	—	43	1	no	—
88	#357	D₄₃	1	1	yes	characteristic, complemented
89	C₄₃	#2206	1	1	yes	characteristic, complemented, Sylow
90	C₂×D₈	—	43	1	no	—
91	C₂×D₈	—	43	1	no	—
92	C₂×D₈	—	86	1	no	—
93	C₂×D₈	C₂×D₄₃	1	1	yes	characteristic
94	#127	—	86	1	no	—
95	C₄×D₄	—	86	1	no	—
96	D₁₆	—	86	2	no	—
97	D₁₆	—	86	2	no	—
98	C₂×C₁₆	—	43	1	no	—
99	C₂×C₁₆	C₂×D₄₃	1	1	yes	characteristic
100	#107	C₂×D₄₃	1	1	yes	characteristic
101	#102	—	86	1	no	—
102	C₄×C₈	—	43	1	no	—
103	C₂×D₄	—	2	1	no	—
104	C₂×D₄	—	86	1	no	—
105	C₂×D₄	—	86	1	no	—
106	C₂×D₄	—	172	1	no	—
107	C₂×D₄	—	172	1	no	—
108	C₂²×C₄	—	172	1	no	—
109	D₈	—	2	1	no	—
110	D₈	—	2	1	no	—
111	D₈	—	43	2	no	—
112	D₈	—	86	1	no	—
113	D₈	—	86	1	no	—
114	D₈	—	86	1	no	—
115	D₈	—	172	2	no	—
116	C₂×C₈	—	43	1	no	—
117	C₂×C₈	C₂²×D₄₃	1	1	yes	characteristic
118	C₄⋊C₄	—	2	1	no	—
119	C₂²⋊C₄	—	172	1	no	—
120	C₄²	—	43	1	no	—
121	C₁₆	—	2	1	no	—
122	C₁₆	—	86	1	no	—
123	C₂³	—	4	1	no	—
124	C₂³	—	172	1	no	—
125	C₂³	—	172	1	no	—
126	D₄	—	4	1	no	—
127	D₄	—	4	1	no	—
128	D₄	—	86	2	no	—
129	D₄	—	344	2	no	—
130	D₄	—	344	2	no	—
131	D₄	—	172	1	no	—
132	D₄	—	172	1	no	—
133	D₄	—	172	1	no	—
134	C₂×C₄	—	4	1	no	—
135	C₂×C₄	—	43	1	no	—
136	C₂×C₄	—	43	1	no	—
137	C₂×C₄	—	344	2	no	—
138	C₂×C₄	D₄×D₄₃	1	1	yes	characteristic
139	C₈	—	86	1	no	—
140	C₈	#10621898	1	1	yes	characteristic
141	C₈	D₄×D₄₃	1	1	yes	characteristic
142	C₂²	—	8	1	no	—
143	C₂²	—	8	1	no	—
144	C₂²	—	8	1	no	—
145	C₂²	—	344	1	no	—
146	C₂²	—	344	1	no	—
147	C₂²	—	344	1	no	—
148	C₂²	—	344	1	no	—
149	C₂²	—	344	1	no	—
150	C₂²	—	172	2	no	—
151	C₂²	D₈×D₄₃	1	1	yes	characteristic
152	C₄	—	8	1	no	—
153	C₄	—	43	2	no	—
154	C₄	—	86	1	no	—
155	C₄	#13063298	1	1	yes	characteristic
156	C₄	#13063352	1	1	yes	characteristic
157	C₂	—	16	1	no	—
158	C₂	—	344	2	no	—
159	C₂	—	688	1	no	—
160	C₂	#14583093	1	1	yes	characteristic
161	C₂	D₁₆×D₄₃	1	1	yes	characteristic
162	C₂	#14583336	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×D₆₈₈

C₂

yes

maximal, characteristic, complemented

C₂×#13063266

C₂

yes

maximal, characteristic, complemented

#14583274

C₂

yes

maximal, characteristic, complemented

#14582981

C₂

yes

maximal, characteristic, complemented

Dic₄₃⋊C₁₆

C₂

yes

maximal, characteristic, complemented

#14582699

C₂

yes

maximal, characteristic, complemented

C₄₃×#357

C₂

yes

maximal, characteristic, complemented

C₂×D₃₄₄

C₂²

yes

characteristic

C₂×D₃₄₄

C₂²

yes

—

—

—

D₆₈₈

—

#13063266

—

C₂×C₄₃⋊C₁₆

C₂²

yes

characteristic

#13063245

—

C₈×Dic₄₃

C₂²

yes

characteristic

C₂×D₈×C₄₃

C₂²

yes

characteristic

C₂×C₁₆×C₄₃

C₂²

yes

characteristic

#107×C₄₃

C₂²

yes

characteristic

C₂×D₄×C₄₃

—

C₂×C₂²⋊D₄₃

—

C₂×C₂²⋊D₄₃

—

C₂×D₁₇₂

—

C₂×D₁₇₂

—

C₂×C₄×D₄₃

—

D₈×C₄₃

—

D₈×C₄₃

—

C₂×C₈×C₄₃

C₂³

yes

characteristic

C₄⋊C₄×C₄₃

—

#10621882

—

(C₂×D₄₃)⋊C₄

—

C₄×Dic₄₃

D₄

yes

characteristic

C₂×C₄₃⋊C₈

D₄

yes

characteristic

D₃₄₄

—

D₃₄₄

—

D₃₄₄

—

D₃₄₄

D₄

yes

complemented

C₁₆×C₄₃

—

C₄₃⋊C₁₆

—

C₂³×C₄₃

—

C₂²×D₄₃

—

C₂²×D₄₃

—

D₄×C₄₃

—

D₄×C₄₃

—

C₂×C₄×C₄₃

—

C₂×C₄×C₄₃

C₂×D₄

yes

characteristic

C₂²⋊D₄₃

—

C₂²⋊D₄₃

—

C₂×Dic₄₃

D₈

yes

characteristic

C₂×Dic₄₃

D₈

yes

characteristic

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

D₁₇₂

—

C₄×D₄₃

—

C₈×C₄₃

C₂×D₄

yes

characteristic

C₈×C₄₃

#41

yes

characteristic

C₄₃⋊C₈

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

—

C₂²×C₄₃

C₂×D₈

yes

characteristic

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₂×D₄₃

—

C₄×C₄₃

—

C₄×C₄₃

yes

C₄×C₄₃

yes

Dic₄₃

—

Dic₄₃

D₁₆

yes

complemented

#2206

—

maximal, Sylow

C₂×C₄₃

—

C₂×C₄₃

#459

yes

characteristic

C₂×C₄₃

C₂×D₁₆

yes

characteristic

C₂×C₄₃

#509

yes

characteristic

D₄₃

—

D₄₃

—

C₂×D₁₆

—

C₂×D₁₆

—

#493

—

C₄×D₈

—

C₄⋊C₁₆

—

#357

—

#357

D₄₃

yes

characteristic, complemented

C₄₃

#2206

yes

characteristic, complemented, Sylow

C₂×D₈

—

C₂×D₈

—

C₂×D₈

—

C₂×D₈

C₂×D₄₃

yes

characteristic

#127

—

C₄×D₄

—

D₁₆

—

D₁₆

—

C₂×C₁₆

—

C₂×C₁₆

C₂×D₄₃

yes

characteristic

100

#107

C₂×D₄₃

yes

characteristic

101

#102

—

102

C₄×C₈

—

103

C₂×D₄

—

104

C₂×D₄

—

105

C₂×D₄

—

106

C₂×D₄

—

172

—

107

C₂×D₄

—

172

—

108

C₂²×C₄

—

172

—

109

D₈

—

110

D₈

—

111

D₈

—

112

D₈

—

113

D₈

—

114

D₈

—

115

D₈

—

172

—

116

C₂×C₈

—

117

C₂×C₈

C₂²×D₄₃

yes

characteristic

118

C₄⋊C₄

—

119

C₂²⋊C₄

—

172

—

120

C₄²

—

121

C₁₆

—

122

C₁₆

—

123

C₂³

—

124

C₂³

—

172

—

125

C₂³

—

172

—

126

D₄

—

127

D₄

—

128

D₄

—

129

D₄

—

344

—

130

D₄

—

344

—

131

D₄

—

172

—

132

D₄

—

172

—

133

D₄

—

172

—

134

C₂×C₄

—

135

C₂×C₄

—

136

C₂×C₄

—

137

C₂×C₄

—

344

—

138

C₂×C₄

D₄×D₄₃

yes

characteristic

139

C₈

—

140

C₈

#10621898

yes

characteristic

141

C₈

D₄×D₄₃

yes

characteristic

142

C₂²

—

143

C₂²

—

144

C₂²

—

145

C₂²

—

344

—

146

C₂²

—

344

—

147

C₂²

—

344

—

148

C₂²

—

344

—

149

C₂²

—

344

—

150

C₂²

—

172

—

151

C₂²

D₈×D₄₃

yes

characteristic

152

C₄

—

153

C₄

—

154

C₄

—

155

C₄

#13063298

yes

characteristic

156

C₄

#13063352

yes

characteristic

157

C₂

—

158

C₂

—

344

—

159

C₂

—

688

—

160

C₂

#14583093

yes

characteristic

161

C₂

D₁₆×D₄₃

yes

characteristic

162

C₂

#14583336

yes

characteristic

	subgroup	G/H
center	C₂²	D₈×D₄₃
commutator	C₂×C₈×C₄₃	C₂³
Frattini	C₂×C₈	C₂²×D₄₃
Fitting	C₄₃×#357	C₂
socle	C₂²×C₄₃	C₂×D₈
hypercenter	#357	D₄₃
hypocenter	C₄₃	#2206
LCS	G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

subgroup

G/H

center

C₂²

D₈×D₄₃

commutator

C₂×C₈×C₄₃

C₂³

Frattini

C₂×C₈

C₂²×D₄₃

Fitting

C₄₃×#357

C₂

socle

C₂²×C₄₃

C₂×D₈

D₄₃

C₄₃

G ▷ C₂×C₈×C₄₃ ▷ C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃

UCS

C₁ ◁ C₂² ◁ C₂×C₄ ◁ C₂×C₈ ◁ #357

N	H ≅ G/N	type
1. C₂×D₆₈₈	C₂	semidirect
2. C₂×#13063266	C₂	semidirect
3. #14583274	C₂	semidirect
4. #14582981	C₂	semidirect
5. Dic₄₃⋊C₁₆	C₂	semidirect
6. #14582699	C₂	semidirect
7. C₄₃×#357	C₂	semidirect
38. D₃₄₄	D₄	semidirect
74. Dic₄₃	D₁₆	semidirect
88. #357	D₄₃	semidirect
89. C₄₃	#2206	semidirect

H ≅ G/N

type

1. C₂×D₆₈₈

C₂

semidirect

2. C₂×#13063266

C₂

semidirect

3. #14583274

C₂

semidirect

4. #14582981

C₂

semidirect

5. Dic₄₃⋊C₁₆

C₂

semidirect

6. #14582699

C₂

semidirect

7. C₄₃×#357

C₂

semidirect

38. D₃₄₄

D₄

semidirect

74. Dic₄₃

D₁₆

semidirect

88. #357

D₄₃

semidirect

89. C₄₃

#2206

semidirect

Subgroups — #19136629

Conjugacy classes of subgroups

Complements